Your father's had a major falling-out with his brother (they were really close). Your parents have taken it really personally and don't want you mixing with your cousins (your uncle's kids) whom you were very close to. They don't want you meeting up every weekend, going to the cinema or out for dinners frequently like you used to. The only contact you are to have with them is during family gatherings like eid, weddings...etc. Your uncle hasn't asked his kids to do the same. The argument between your parents and your uncle has nothing to do with you kids.

What do you do? Do you cut off all ties with your uncle and cousins, knowing that your parents and uncle are unlikely to make up in the foreseeable future, or do you ignore what your parents have asked you to do and continue with your life as it used to be?

I think that, your parents problems are their own and your relationship with your cousins has nothing to do with them or your uncle & aunt. After explaining to your parents that the fight has nothing to do with you and that you do not want to diminish the blood ties you grew up with, you should continue to be close to your family. Parents should not live through their kids, the kids need to have their own lives and live according to their own choices.

I will ignore whatever my parents tell me about not mixing with my cousins..but if my cousins are really bad I mean if they drink or behaving very bad ..ofcourse I'll listen to my parents.

I will try to talk my father from it .. telling him that no matter what, we are family .. and we should be close to each other and all ..

if it didnt work, then I guess not to upset him I wouldnt just go aginst him coz it will make hate between the family even more .. but I will communicate my will to keep in contact to my cousins .. we will try to find a way that wouldnt upset both sides .. and we would just to solve those problems between them.

i'd reason with him, and let him know that i am not part of this fight, and he should fights his own battles.
as enigma said, it has nothing to do with the children.
so id hang out with my cousins.

Cutting the family ties is against Islam teachings, the only thing to do in such suitation is to continue the relations but in the background mostly to avoide any further problems.